Model reduction in stochastic environments

E. Forgoston; L. Billings; I. B. Schwartz

doi:10.1142/9789811200359_0003

Model reduction in stochastic environments

E. Forgoston, L. Billings, I. B. Schwartz

Applied Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We present a general theory of stochastic model reduction which is based on a normal form coordinate transform method of A. J. Roberts. This nonlinear, stochastic projection allows for the deterministic and stochastic dynamics to interact correctly on the lower-dimensional manifold so that the dynamics predicted by the reduced, stochastic system agrees well with the dynamics predicted by the original, high-dimensional stochastic system. The method may be applied to any system with well-separated time scales. In this article, we consider a physical problem that involves a singularly perturbed Duffing oscillator as well as a biological problem that involves the prediction of infectious disease outbreaks.

Original language	English
Title of host publication	Stochastic Pdes And Modelling Of Multiscale Complex System
Publisher	World Scientific Publishing Co.
Pages	37-61
Number of pages	25
ISBN (Electronic)	9789811200359
DOIs	https://doi.org/10.1142/9789811200359_0003
State	Published - 1 Jan 2019

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Model reduction in stochastic environments

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